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High Energy Physics - Theory

arXiv:2111.02410 (hep-th)
[Submitted on 3 Nov 2021 (v1), last revised 25 Mar 2022 (this version, v2)]

Title:Introduction to Monte Carlo for Matrix Models

Authors:Raghav G. Jha
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Abstract:We consider a wide range of matrix models and study them using the Monte Carlo technique in the large $N$ limit. The results we obtain agree with exact analytic expressions and recent numerical bootstrap methods for models with one and two matrices. We then present new results for several unsolved multi-matrix models where no other tool is yet available. In order to encourage an exchange of ideas between different numerical approaches to matrix models, we provide programs in Python that can be easily modified to study potentials other than the ones discussed. These programs were tested on a laptop and took between a few minutes to several hours to finish depending on the model, $N$, and the required precision.
Comments: v2: Added some more text and references, 55 pages, 63 references, 15 figures. All else same as v1. To be published in SciPost Physics Lecture Notes. v1: 52 pages with a few Mathematica codes, 3 Python codes, 5 tables, 10 exercises, 14 figures, and 52 references
Subjects: High Energy Physics - Theory (hep-th); High Energy Physics - Lattice (hep-lat); Computational Physics (physics.comp-ph)
Cite as: arXiv:2111.02410 [hep-th]
  (or arXiv:2111.02410v2 [hep-th] for this version)
  https://doi.org/10.48550/arXiv.2111.02410
Journal reference: SciPost Phys. Lect. Notes 46 (2022)
Related DOI: https://doi.org/10.21468/SciPostPhysLectNotes.46

Submission history

From: Raghav Govind Jha [view email]
[v1] Wed, 3 Nov 2021 18:00:00 UTC (2,326 KB)
[v2] Fri, 25 Mar 2022 17:52:36 UTC (2,362 KB)
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